Kapitza inverted pendulum

What you are seeing: a rigid pendulum whose pivot moves vertically at $y_p(t) = a \cos(\omega t)$. The natural unstable equilibrium (pendulum upside-down) becomes STABLE when the drive is strong enough: $a^2 \omega^2 / (2 g l) \gt 1$. Below threshold the pendulum falls; above, it bobs around the upside-down equilibrium.

Adjust $a$ (amplitude) and $\omega$ (frequency). The stability indicator turns green when $a^2 \omega^2 \gt 2 g l$. The yellow effective potential $U_\text{eff}(\theta) = -m g l \cos\theta + \frac{1}{4} m (a \omega)^2 \sin^2\theta$ has a minimum at $\theta = 0$ (upside-down) once stability is achieved.